When to use the law of cosines?

1. Oct 15, 2015

student1856

In Griffith's Introduction to electrodynamics, he uses a cursive r as the distance between a charge and a test point. most of the time to find this distance we subtract the two position vectors and find the magnitude, but occasionally we use the law of cosines. Now yes I know we use the law of cosines when the angle is not 90 degrees in statics problems. So I assumed that was the indicator to when to use the law of cosines. However immediately after assuming this, we just subtracted a second set of vectors and found the magnitude of two vectors that didnt make a right triangle. Can someone just very clearly and slowly tell me when to use the law of cosines, and when i can just subtract two vectors and find the magnitude?

2. Oct 15, 2015

SteamKing

Staff Emeritus
It's not clear what you are talking about here.

If you subtract two position vectors, you're going to wind up with a third vector, not a magnitude.

If you can provide some clear examples of what confuses you, for those of us who may not have a copy of Griffith's, that would be helpful.

3. Oct 15, 2015

Geofleur

You can always just subtract two vectors and find the magnitude. You can even prove the law of cosines that way. Let $\mathbf{A}$ and $\mathbf{B}$ be vectors. Then $(\mathbf{A}-\mathbf{B})\cdot(\mathbf{A}-\mathbf{B}) = | \mathbf{A} - \mathbf{B} |^2 = A^2 + B^2 - 2AB\cos \theta$, where $\theta$ is the angle between the vectors when they are placed tail-to-tail. From a picture of the triangle formed from $\mathbf{A}$, $\mathbf{B}$, and $\mathbf{A}-\mathbf{B}$, we recognize this equation as none other than the law of cosines.

4. Oct 25, 2015

mathwonk

of course the fact you are apparently using that A.B = |A||B| cos(theta) is equivalent to the law of cosines.